1.

Find the electric field potentail and strength at the centre of a hemisphere fo raidus `R` ahcged uniformly with the the surface density `sigma`.A. `(sigmaR)/(epsilon_(0)`B. `(2sigmaR)/(epsilon_(0))`C. `(sigmaR)/(2epsilon_(0))`D. `(sigmaR)/(3epsilon_(0))`

Answer» Correct Answer - A
The area of shaded element is `dA=2pirRd theta`
`=2piR^(2)sintheta d theta rArr dV=(1)/(4piepsilon_(0))(dq)/(R)`
`=(1)/(4piepsilon_(0))(sigma2piR^(2)sinthetad theta)/(R)=(sigma R)/(2epsilon_(0))sinthetad theta`
`V=(sigmaR)/(2epsilon_(0))int_(0)^(pi//2)sintheta d theta =(sigmaR)/(2epsilon_(0))`


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